As a wound heals, or a body plan forms, or a tumour invades, observed cellular motions within the advancing cell swarm are thought to stem from yet to be observed physical stresses that act in some direct and causal mechanical fashion. Here we show that such a relationship between motion and stress is far from direct. Using monolayer stress microscopy, we probed migration velocities, cellular tractions and intercellular stresses in an epithelial cell sheet advancing towards an island on which cells cannot adhere. We found that cells located near the island exert tractions that pull systematically towards this island regardless of whether the cells approach the island, migrate tangentially along its edge, or paradoxically, recede from it. This unanticipated cell-patterning motif, which we call kenotaxis, represents the robust and systematic mechanical drive of the cellular collective to fill unfilled space.